Quark model

**Figure 1**: The pseudoscalar meson nonet. Members of the original meson "octet" are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet, the Eightfold Way name derives from the patterns of eight for the mesons and baryons in the original classification scheme.

In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks that give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental verification beginning in the late 1960s and is a valid and effective classification of them to date. The model was independently proposed by physicists Murray Gell-Mann,^[1] who dubbed them "quarks" in a concise paper, and George Zweig,^[2]^[3] who suggested "aces" in a longer manuscript. André Petermann also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation.^[4]^[5] Today, the model has essentially been absorbed as a component of the established quantum field theory of strong and electroweak particle interactions, dubbed the Standard Model.

Hadrons are not really "elementary", and can be regarded as bound states of their "valence quarks" and antiquarks, which give rise to the quantum numbers of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the Poincaré symmetry—J^PC, where J, P and C stand for the total angular momentum, P-symmetry, and C-symmetry, respectively.

The other set is the flavor quantum numbers such as the isospin, strangeness, charm, and so on. The strong interactions binding the quarks together are insensitive to these quantum numbers, so variation of them leads to systematic mass and coupling relationships among the hadrons in the same flavor multiplet.

All quarks are assigned a baryon number of 1/3. Up, charm and top quarks have an electric charge of +2/3, while the down, strange, and bottom quarks have an electric charge of −1/3. Antiquarks have the opposite quantum numbers. Quarks are spin-1/2 particles, and thus fermions. Each quark or antiquark obeys the Gell-Mann–Nishijima formula individually, so any additive assembly of them will as well.

Mesons are made of a valence quark–antiquark pair (thus have a baryon number of 0), while baryons are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavors of quark (which form an approximate flavor SU(3) symmetry). There are generalizations to larger number of flavors.

^ Gell-Mann, M. (4 January 1964). "A Schematic Model of Baryons and Mesons". Physics Letters. 8 (3): 214–215. Bibcode:1964PhL.....8..214G. doi:10.1016/S0031-9163(64)92001-3.
^ Zweig, G. (17 January 1964). An SU(3) Model for Strong Interaction Symmetry and its Breaking (PDF) (Report). CERN Report No.8182/TH.401.
^ Zweig, G. (1964). An SU(3) Model for Strong Interaction Symmetry and its Breaking: II (PDF) (Report). CERN Report No.8419/TH.412.
^ Petermann, A. (1965). "Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels" [Strangeness properties and a mass formula for vector meson]. Nuclear Physics. 63 (2): 349–352. arXiv:1412.8681. Bibcode:1965NucPh..63..349P. doi:10.1016/0029-5582(65)90348-2.
^ Petrov, Vladimir A. (June 23–27, 2014). Half a Century with QUARKS. XXX-th International Workshop on High Energy Physics. Protvino, Moscow Oblast, Russia. arXiv:1412.8681.

[Gell-Man1964-1] Gell-Mann, M. (4 January 1964). "A Schematic Model of Baryons and Mesons". Physics Letters. 8 (3): 214–215. Bibcode:1964PhL.....8..214G. doi:10.1016/S0031-9163(64)92001-3.

[Zweig1964a-2] Zweig, G. (17 January 1964). An SU(3) Model for Strong Interaction Symmetry and its Breaking (PDF) (Report). CERN Report No.8182/TH.401.

[Zweig1964b-3] Zweig, G. (1964). An SU(3) Model for Strong Interaction Symmetry and its Breaking: II (PDF) (Report). CERN Report No.8419/TH.412.

[4] Petermann, A. (1965). "Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels" [Strangeness properties and a mass formula for vector meson]. Nuclear Physics. 63 (2): 349–352. arXiv:1412.8681. Bibcode:1965NucPh..63..349P. doi:10.1016/0029-5582(65)90348-2.

[5] Petrov, Vladimir A. (June 23–27, 2014). Half a Century with QUARKS. XXX-th International Workshop on High Energy Physics. Protvino, Moscow Oblast, Russia. arXiv:1412.8681.

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